Bayesian Networks: P(a,b,c,d) Calculation

[prashantgolu]

suppose i have 2 bayesian networks...
a->b and c->d ie b depends on a and d depends on b
now P(a,b,c,d)=P(a)*P(b|a)*P(c|a,b)*P(d|a,b,c)
=P(a)*P(b|a)*P(c)*P(d|c)

Am i right...?
please reply..i need it as quickly as possible...

 

[SW VandeCarr]

suppose i have 2 bayesian networks...
a->b and c->d ie b depends on a and d depends on b
now P(a,b,c,d)=P(a)*P(b|a)*P(c|a,b)*P(d|a,b,c)
=P(a)*P(b|a)*P(c)*P(d|c)

Am i right...?
please reply..i need it as quickly as possible...

It's not clear what you are trying to say since the term on the left is not a conditional probability.

Note: $$P(A|B,C,D)= \frac{A\cap (B\cup C\cup D)}{B\cup C\cup D}$$

 

[prashantgolu]

By ',' i mean intersection
P(x,y)=p(x|y)*p(y)
like this...

 

[SW VandeCarr]

suppose i have 2 bayesian networks...
a->b and c->d ie b depends on a and d depends on b
now P(a,b,c,d)=P(a)*P(b|a)*P(c|a,b)*P(d|a,b,c)
=P(a)*P(b|a)*P(c)*P(d|c)

Am i right...?
please reply..i need it as quickly as possible...

OK, then the first line looks correct. However I don't know how the assumptions you're making regarding conditional independence allow you to get your simplification on the second line. If the two networks (a,b), (c,d) are conditionally independent, then I believe your simplifications are correct if they are taken individually. However, I'm not sure why you would combine them since they have no common variables.

EDIT: In other words, am I supposed to know that P(c|a,b)=P(c)? How does the fact that d depends on c tell me that? (I assume that you made a mistake when you stated d depends on b since your formula indicates d depends on c.)

 

[blue_raver22]

Yes, you are correct in your calculation for P(a,b,c,d) in this specific scenario. However, it is important to note that Bayesian networks can have more complex structures and dependencies, so this formula may not always apply. It is always best to carefully analyze the structure of the network and the conditional probabilities before making any calculations. Additionally, it is important to verify that all the probabilities used in the calculation are accurate and consistent.